Finding an optimal decision tree for a supervised learning task is a challenging combinatorial problem to solve at scale. It was recently proposed to frame the problem as a Markov Decision Problem (MDP) and use deep reinforcement learning to tackle scaling. Unfortunately, these methods are not competitive with the current branch-and-bound state-of-the-art. We propose instead to scale the resolution of such MDPs using an information-theoretic tests generating function that heuristically, and dynamically for every state, limits the set of admissible test actions to a few good candidates. As a solver, we show empirically that our algorithm is at the very least competitive with branch-and-bound alternatives. As a machine learning tool, a key advantage of our approach is to solve for multiple complexity-performance trade-offs at virtually no additional cost. With such a set of solutions, a user can then select the tree that generalizes best and which has the interpretability level that best suits their needs, which no current branch-and-bound method allows.

Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for NP-hard/complete problems by learning to generate superior solutions solely from training data. Current neural-based methods for solving CO problems often overlook the inherent "algorithmic" nature of the problems. In contrast, heuristics designed for CO problems, e.g. TSP, frequently leverage well-established algorithms, such as those for finding the minimum spanning tree. In this paper, we propose leveraging recent advancements in neural algorithmic reasoning to improve the learning of CO problems. Specifically, we suggest pre-training our neural model on relevant algorithms before training it on CO instances. Our results demonstrate that by using this learning setup, we achieve superior performance compared to non-algorithmically informed deep learning models.

In decision-making problems with limited training data, policy functions approximated using deep neural networks often exhibit suboptimal performance. An alternative approach involves learning a world model from the limited data and determining actions through online search. However, the performance is adversely affected by compounding errors arising from inaccuracies in the learnt world model. While methods like TreeQN have attempted to address these inaccuracies by incorporating algorithmic structural biases into their architectures, the biases they introduce are often weak and insufficient for complex decision-making tasks. In this work, we introduce Differentiable Tree Search (DTS), a novel neural network architecture that significantly strengthens the inductive bias by embedding the algorithmic structure of a best-first online search algorithm. DTS employs a learnt world model to conduct a fully differentiable online search in latent state space. The world model is jointly optimised with the search algorithm, enabling the learning of a robust world model and mitigating the effect of model inaccuracies. We address potential Q-function discontinuities arising from naive incorporation of best-first search by adopting a stochastic tree expansion policy, formulating search tree expansion as a decision-making task, and introducing an effective variance reduction technique for the gradient computation. We evaluate DTS in an offline-RL setting with a limited training data scenario on Procgen games and grid navigation task, and demonstrate that DTS outperforms popular model-free and model-based baselines.

Utilizing unsupervised representation learning for quantum architecture search (QAS) represents a cutting-edge approach poised to realize potential quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices. QAS is a scheme to design quantum circuits for variational quantum algorithms (VQAs). Most QAS algorithms combine their search space and search algorithms together and thus generally require evaluating a large number of quantum circuits during the search process, which results in formidable computational demands and limits their applications to large-scale quantum circuits. Predictor-based QAS algorithms can alleviate this problem by directly estimating the performance of circuits according to their structures. However, a high-performance predictor generally requires very time-consuming labeling to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to their ground-truth performances. Recently, a classical neural architecture search algorithm Arch2vec inspires us by showing that architecture search can benefit from decoupling unsupervised representation learning from the search process. Whether unsupervised representation learning can help QAS without any predictor is still an open topic. In this work, we propose a framework QAS with unsupervised representation learning and visualize how unsupervised architecture representation learning encourages quantum circuit architectures with similar connections and operators to cluster together. Specifically, our framework enables the process of QAS to be decoupled from unsupervised architecture representation learning so that the learned representation can be directly applied to different downstream applications. Furthermore, our framework is predictor-free eliminating the need for a large number of labeled quantum circuits.

A fundamental (and largely open) challenge in sequential decision-making is dealing with non-stationary environments, where exogenous environmental conditions change over time. Such problems are traditionally modeled as non-stationary Markov decision processes (NSMDP). However, existing approaches for decision-making in NSMDPs have two major shortcomings: first, they assume that the updated environmental dynamics at the current time are known (although future dynamics can change); and second, planning is largely pessimistic, i.e., the agent acts ``safely'' to account for the non-stationary evolution of the environment. We argue that both these assumptions are invalid in practice -- updated environmental conditions are rarely known, and as the agent interacts with the environment, it can learn about the updated dynamics and avoid being pessimistic, at least in states whose dynamics it is confident about. We present a heuristic search algorithm called \textit{Adaptive Monte Carlo Tree Search (ADA-MCTS)} that addresses these challenges. We show that the agent can learn the updated dynamics of the environment over time and then act as it learns, i.e., if the agent is in a region of the state space about which it has updated knowledge, it can avoid being pessimistic. To quantify ``updated knowledge,'' we disintegrate the aleatoric and epistemic uncertainty in the agent's updated belief and show how the agent can use these estimates for decision-making. We compare the proposed approach with the multiple state-of-the-art approaches in decision-making across multiple well-established open-source problems and empirically show that our approach is faster and highly adaptive without sacrificing safety.

Bayesian Optimization (BO) is a powerful method for optimizing black-box functions by combining prior knowledge with ongoing function evaluations. BO constructs a probabilistic surrogate model of the objective function given the covariates, which is in turn used to inform the selection of future evaluation points through an acquisition function. For smooth continuous search spaces, Gaussian Processes (GPs) are commonly used as the surrogate model as they offer analytical access to posterior predictive distributions, thus facilitating the computation and optimization of acquisition functions. However, in complex scenarios involving optimizations over categorical or mixed covariate spaces, GPs may not be ideal. This paper introduces Simulation Based Bayesian Optimization (SBBO) as a novel approach to optimizing acquisition functions that only requires \emph{sampling-based} access to posterior predictive distributions. SBBO allows the use of surrogate probabilistic models tailored for combinatorial spaces with discrete variables. Any Bayesian model in which posterior inference is carried out through Markov chain Monte Carlo can be selected as the surrogate model in SBBO. In applications involving combinatorial optimization, we demonstrate empirically the effectiveness of SBBO method using various choices of surrogate models.

MaxSAT is an optimization version of the famous NP-complete Satisfiability problem (SAT). Algorithms for MaxSAT mainly include complete solvers and local search incomplete solvers. In many complete solvers, once a better solution is found, a Soft conflict Pseudo Boolean (SPB) constraint will be generated to enforce the algorithm to find better solutions. In many local search algorithms, clause weighting is a key technique for effectively guiding the search directions. In this paper, we propose to transfer the SPB constraint into the clause weighting system of the local search method, leading the algorithm to better solutions. We further propose an adaptive clause weighting strategy that breaks the tradition of using constant values to adjust clause weights. Based on the above methods, we propose a new local search algorithm called SPB-MaxSAT that provides new perspectives for clause weighting on MaxSAT local search solvers. Extensive experiments demonstrate the excellent performance of the proposed methods.

Many real-world problems can be efficiently modeled as Mixed Integer Programs (MIPs) and solved with the Branch-and-Bound method. Prior work has shown the existence of MIP backdoors, small sets of variables such that prioritizing branching on them when possible leads to faster running times. However, finding high-quality backdoors that improve running times remains an open question. Previous work learns to estimate the relative solver speed of randomly sampled backdoors through ranking and then decide whether to use it. In this paper, we utilize the Monte-Carlo tree search method to collect backdoors for training, rather than relying on random sampling, and adapt a contrastive learning framework to train a Graph Attention Network model to predict backdoors. Our method, evaluated on four common MIP problem domains, demonstrates performance improvements over both Gurobi and previous models.

End-to-end (E2E) automatic speech recognition (ASR) methods exhibit remarkable performance. However, since the performance of such methods is intrinsically linked to the context present in the training data, E2E-ASR methods do not perform as desired for unseen user contexts (e.g., technical terms, personal names, and playlists). Thus, E2E-ASR methods must be easily contextualized by the user or developer. This paper proposes an attention-based contextual biasing method that can be customized using an editable phrase list (referred to as a bias list). The proposed method can be trained effectively by combining a bias phrase index loss and special tokens to detect the bias phrases in the input speech data. In addition, to improve the contextualization performance during inference further, we propose a bias phrase boosted (BPB) beam search algorithm based on the bias phrase index probability. Experimental results demonstrate that the proposed method consistently improves the word error rate and the character error rate of the target phrases in the bias list on both the Librispeech-960 (English) and our in-house (Japanese) dataset, respectively.

Generalized Nested Rollout Policy Adaptation (GNRPA) is a Monte Carlo search algorithm for optimizing a sequence of choices. We propose to improve on GNRPA by avoiding too deterministic policies that find again and again the same sequence of choices. We do so by limiting the number of repetitions of the best sequence found at a given level. Experiments show that it improves the algorithm for three different combinatorial problems: Inverse RNA Folding, the Traveling Salesman Problem with Time Windows and the Weak Schur problem.